Advanced Statistical Inference for Stochastic Quasi-Reaction Systems

Quasi-reaction systems are often modelled with stochastic differential equations in order to capture the inherent randomness of their dynamics. The traditional local linear approximation methods for the estimation of the reaction rates face significant challenges in certain conditions. When the system is observed at short intervals, high correlations between successive observations result in numerical instability, while measurements at wider intervals lead to biased estimates of the parameters. This thesis addresses these issues with the development of novel inferential procedures. First, we introduce a latent event history model, by formalizing a latent space of unobserved reactions and their connection with the observed states. Under this framework, the system parameters can be estimated via a modified Expectation-Maximisation algorithm, with an extended Kalman filter at the E-step for reconstructing the underlying latent states. The approach is shown to be more accurate than existing methods, particularly for observations measured at short time intervals. In order to model more complex scenarios, the method is further extended to account for external time-varying factors that may affect the reaction rates of the system. As a second inferential approach, we concentrate on the mean of the dynamics and propose a novel mean-field approximation method. The method exploits the analytical solution of the ordinary differential equations in the case of unitary systems to propose an approximate solution for a generic quasi-reaction system. Besides a high computational efficiency, the resulting approach is found to perform particularly well when the measurements of the system are taken at wide time intervals. Finally, we provide an illustration of the proposed inferential procedures on the modelling of COVID-19 transmission and cell differentiation.